Coordinating Feet in Bipedal Balance

Biomechanical models of human standing balance in the sagittal plane typically treat the two ankle joints as a single degree of freedom. They describe the sum of the torques produced by the ankles, but do not predict what the contribution of each ankle will be. Similarly, balance algorithms for bipedal robots control the location of the overall center of pressure, but do not consider the individual centers of pressure under each foot. We present theoretical and experimental results showing an optimal solution to the problem of producing a single desired torque with redundant actuators, resulting in alignment of the individual centers of pressure under each foot. This produces a feedback gain structure not addressed in the biomechanics literature and a balance controller that is potentially more robust to unexpected changes in the region of support. We show that the feedback gain matrix of this controller has an unexpected structure — large off-axis integral gain elements indicate that the ankle torque that equalize the position of the center of pressure is determined primarily by information from the other foot. We also demonstrate controllers based on this design using the Sarcos Primus hydraulic biped.